Right Angle: If inscribed angle intercepts semicircle, the angle is a right angle.
Arc-Intercept: If two inscribed angles intercept the same arc, they have the same measure.
arc intercept
Theorem 1- If a tangent and a chord intersect a circle at the point of tangency, the measure of that angle is half the measure of the arc.
Theorem 2- angles formed by 2 secants that intersect in the interior of the circle equal half of the sum of the intercepted angles
Theorem 3- the measure of an angle formed by 2 secants that intersect in the exterior of a circle is half the measures of the intercepted arc Theorem 4- measure of a secant tangent angle with its vertex outside the circle is .5 the difference of the measures of the intercepted arcs
Theorem 5- measure of a tangent-tangent angle with its vertex outside the circle is .5 the difference of the measures of the intercepted arcs, or the measure of the major arc is minus 180 degrees
Inscribed angle theorem: The measure of an angle inscribed in a circle is equal to one half the measure of the intercepted arc.
Question: What is the measure of an incribed angle that intercepts a semicircle?
Inscribed angle: is an angle whose vertex lies on a circle and whose sides are chords of the circle.
Intercepted arc: arc whose endpoints lie on the sides of an inscribed angle.
Right-Angle Corollary= if an inscirbed angle intercepts a semicircle, then the angle is a right angle.
Arc-Intercept Corollary= if two inscribed angles intercept the same arc, then they have the same measure.
[[image:U:\math\2.bmp width="146" height="156" caption="external image"]][[image:U:\math\1.bmp width="145" height="152" caption="external image"]][[image:U:\math\3.bmp width="172" height="162" caption="external image"]]
Arc-Intercept: If two inscribed angles intercept the same arc, they have the same measure.
Theorem 1- If a tangent and a chord intersect a circle at the point of tangency, the measure of that angle is half the measure of the arc.
Theorem 2- angles formed by 2 secants that intersect in the interior of the circle equal half of the sum of the intercepted angles
Theorem 3- the measure of an angle formed by 2 secants that intersect in the exterior of a circle is half the measures of the intercepted arc
Theorem 4- measure of a secant tangent angle with its vertex outside the circle is .5 the difference of the measures of the intercepted arcs
Theorem 5- measure of a tangent-tangent angle with its vertex outside the circle is .5 the difference of the measures of the intercepted arcs, or the measure of the major arc is minus 180 degrees
Inscribed angle theorem: The measure of an angle inscribed in a circle is equal to one half the measure of the intercepted arc.
Question: What is the measure of an incribed angle that intercepts a semicircle?
Inscribed angle: is an angle whose vertex lies on a circle and whose sides are chords of the circle.
Intercepted arc: arc whose endpoints lie on the sides of an inscribed angle.
Right-Angle Corollary= if an inscirbed angle intercepts a semicircle, then the angle is a right angle.
Arc-Intercept Corollary= if two inscribed angles intercept the same arc, then they have the same measure.
[[image:U:\math\2.bmp width="146" height="156" caption="external image"]][[image:U:\math\1.bmp width="145" height="152" caption="external image"]][[image:U:\math\3.bmp width="172" height="162" caption="external image"]]
X= A+Y devided by 2 X=Y-A devided by 2 x=Y/2